Abstract:

       We generalize the concepts of some (∈，∈∨q)- fuzzy subsets to Γ- semigroups. We also introduce the concept of (∈，∈∨q)- fuzzy Γ- subsemigroup,(∈，∈∨q)- fuzzy bi-ideal and (∈，∈∨q)- fuzzy generalized bi-ideal into Γ- semigroups, and address their expressions with some theories of fuzzy sets. It is proved that the intersection and union of (∈，∈∨q)- fuzzy bi-ideals are still (∈，∈∨q)- fuzzy bi-ideals, and that every (∈，∈∨q)- fuzzy generalized bi-ideal of regular Γ- semigroups is a (∈，∈∨q)- fuzzy bi-ideal.

Key words: Γ-semigroup, (∈, ∈∨q)-fuzzy bi-ideals, fuzzy point